Season the beef with salt and pepper. Combine the soy sauce, ginger, garlic, 1 tablespoon rice vinegar, and 1 tablespoon orange juice in a shallow dish. Add the beef, turn to coat, and marinate at room temperature for 15 minutes. Meanwhile, rub the olive oil into a cast-iron skillet and place over high heat. When the skillet is heated through, place the beef in the skillet and sear for 2 minutes per side. Remove to a cutting board to rest for 5 minutes.
Place the orange slices in the pan in batches and sear for 30 seconds on each side. Remove to a plate.
Meanwhile, in a large bowl, whisk together the remaining orange juice and vinegar and salt and pepper. Add the arugula and toss to coat.
Slice the beef tournedos into 1/2-inch-thick slices. To serve, place a handful of arugula on each of 4 plates, arrange 3 orange slices over the arugula, and top with sliced beef. Season with freshly ground pepper and serve.